Developing steady laminar flow through uniform straight tubes with varying wall cross curvature

Numerical calculations are used to determine not only the wall shear stress but also the entry length in a laminar steady flow of an incompressible Newtonian fluid. The fluid is conveyed through rigid straight tubes with axially uniform cross sections, which mimic collapsed vessels. For each tube configuration, the "Navier-Stokes" equations are solved using the finite element method. The numerical tests are performed with the same value of the volume flow-rate whatever the tube configuration for three "Reynolds numbers". The wall shear stress is computed and determined along the axis of the tube, then the entry length is estimated by introducing two indexes by using: (i) the axial fluid velocity, and (ii) the wall shear stress. The results are analysed in order to exhibit the mechanical environment of cultured endothelial cells in the flow chamber for which the test conditions will be well-defined. For example, in a tube configuration where the opposite walls are in contact for which the inner perimeter and the area of the cross section are respectively given by 45 mm and 37.02 mm(2), the computed entry lengths with the criteria defined by (i) and (ii) are equals to about 118 and 126 mm, respectively for R(e0) = 500.